相关论文: On a Class of Quantum Canonical Transformations an…
The quantization of the forced harmonic oscillator is studied with the quantum variable ($x,\hat v$), with the commutation relation $[x,\hat v]=i\hbar/m$, and using a Shr\"odinger's like equation on these variable, and associating a linear…
In this work we present the simplest generic form of the propagator for the time-dependent quadratic Hamiltonian. We manifest the simplicity of our method by giving explicitly the propagators for a free particle in time-dependent electric…
In quantum physics the free particle and the harmonically trapped particle are arguably the most important systems a physicist needs to know about. It is little known that, mathematically, they are one and the same. This knowledge helps us…
In order to evaluate the Feynman path integral in noncommutative quantum mechanics, we consider properties of a Lagrangian related to a quadratic Hamiltonian with noncommutative spatial coordinates. A quantum-mechanical system with…
Canonical transformation in a three-dimensional phase space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed as based on canonoid transformations. It is shown that…
We carry out an exact quantization of a PT symmetric (reversible) Li\'{e}nard type one dimensional nonlinear oscillator both semiclassically and quantum mechanically. The associated time independent classical Hamiltonian is of non-standard…
An exact invariant is derived for three-dimensional Hamiltonian systems of $N$ particles confined within a general velocity-independent potential. The invariant is found to contain a time-dependent function $f_{2}(t)$, embodying a solution…
In this work, we investigate the photoionization cross-section of an electron confined in a quantum dot, considering the position-dependent variation of the effective mass through the parameter $\gamma$. We used a theoretical model based on…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless''…
We discuss canonical transformations in Quantum Field Theory in the framework of the functional-integral approach. In contrast with ordinary Quantum Mechanics, canonical transformations in Quantum Field Theory are mathematically more subtle…
We study the behavior of a quantum particle trapped in a confining potential in one dimension under multiple sudden changes of velocity and/or acceleration. We develop the appropriate formalism to deal with such situation and we use it to…
We calculate the quantum corrections to the classical action of a particle with coordinate-dependent mass. The result is made self-consistent by a variational approach, thus making it applicable to strong-couplings and singular potentials.…
This paper is devoted to find the exact solution of the harmonic oscillator in a position-dependent 4-dimensional noncommutative phase space. The noncommutative phase space that we consider is described by the commutation relations between…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…
We argue that correct account of the quantum properties of macroscopic objects which form reference frames (RF) demand the change of the standard space-time picture accepted in Quantum Mechanics. Galilean or Lorentz space-time…
We show how a large family of master equations, describing quantum Brownian motion of a harmonic oscillator with translationally invariant damping, can be derived within a phenomenological approach, based on the assumption that an…
The quadrature distribution for the quantum damped oscillator is introduced in the framework of the formulation of quantum mechanics based on the tomography scheme. The probability distribution for the coherent and Fock states of the damped…
A certain notion of canonical equivalence in quantum mechanics is proposed. It is used to relate quantal systems with discrete ones. Discrete systems canonically equivalent to the celebrated harmonic oscillator as well as the quartic and…
In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over…
We investigate a model system consisting of a Morse oscillator strongly coupled to a doubly-degenerate bending degree of freedom and show that Canonical Perturbation Theory is able to provide a fairly precise, though not exact,…